Cremona's table of elliptic curves

2112 = 2⁶ · 3 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+	Signs for the Atkin-Lehner involutions
Class	2112k	Isogeny class
Conductor	2112	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	2364899328 = 215 · 38 · 11	Discriminant
Eigenvalues	2+ 3-  2  0 11+  6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-577,4607]	[a1,a2,a3,a4,a6]
j	649461896/72171	j-invariant
L	2.8152235157898	L(r)(E,1)/r!
Ω	1.4076117578949	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2112f3 1056c3 6336bc3 52800g4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2112k3

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	2	0	+	6	2	-4	4	-2	4	2	10	-4	4	-6	-12	6	-4	4	10	16	4	10	2

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Quadratic twists for elliptic curve 2112k3

-4	8	-3	5	-7	-11
2112f3	1056c3	6336bc3	52800g4	103488bf4	23232bx4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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